mcas sample essays grade 7

Student Writing Lessons | Student Writing Samples | MCAS | Response to Text

MCAS Writing - Student Samples by Grade Level

Read Time 1 mins | Dec 21, 2020 1:52:08 PM | Written by: Toolbox

These released item samples from the https://www.doe.mass.edu/ are analyzed for specific skills taught using the Empowering Writers approach. Each sample features the skills that the students successfully applied and suggestions for improvement. Feel free to download each sample and use it as a guide to analyze your own student samples. As assessment time nears, these will provide you with specific feedback for your students as well as point you in the direction of the most effective lessons. 

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How to Write an MCAS Essay in Five Hours

Last Updated: December 15, 2022 References

This article was co-authored by Stephanie Wong Ken, MFA . Stephanie Wong Ken is a writer based in Canada. Stephanie's writing has appeared in Joyland, Catapult, Pithead Chapel, Cosmonaut's Avenue, and other publications. She holds an MFA in Fiction and Creative Writing from Portland State University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 15,145 times.

The Massachusetts Comprehensive Assessment System (MCAS) is a state wide standards based assessment program developed in Massachusetts as a result of the Education Reform Law of 1993. All students who are in public schooling in Massachusetts from grade 3 to grade 10 are required to take MCAS. The goal of the MCAS is to measure student performance based on the Massachusetts Curriculum Framework learning standards and to report on the performance of individual students in schools and districts in Massachusetts. As a Massachusetts public school student, you are required to pass the grade 10 tests in English Language Arts (ELA), Mathematics, and one of the four high school Science and Technology Engineering tests to be eligible for your high school diploma.

Preparing to write the MCAS Essay

• Your MCAS essay should be free of any grammatical or spelling errors and present fully developed ideas in the five paragraph format.

• To achieve a high 6 in the Topic/Idea development category, you will need to demonstrate rich topic/idea development, careful and subtle organization, and use language effectively in your essay. You will earn a low 1 if your essay has very little topic/idea development, organization or details, and you demonstrate very little awareness of your audience or of the task asked of you in the essay prompt.
• To achieve a high 4 in the Standard English conventions category, you will need to demonstrate control of sentence structure, grammar and usage. Your essay should also be long enough to show you have a strong grasp of complex sentence structure and standard English conventions. You will earn a low 1 if your essay contain errors that interfere with clear communication and understanding in a serious way, and you have very little control of sentence structure, grammar, and usage.
• Detailed information on the scoring guides for each category can be found at http://www.doe.mass.edu/mcas/student/2014/question.aspx?GradeID=10&SubjectCode=ela&QuestionID=33209# .

• You may receive a prompt that focuses on the use of a technique in writing, for example: “Select a work of literature you have read in or out of school in which there
is a difference between what is expected and what actually happens. In a well-developed composition, explain the situation and tell why it is important to the work you have chosen.”
• You may receive a prompt that focuses on the use of a motif in writing, for example: “From a work of literature you have read in or out of school, select a character that, in your opinion, is heroic. In a well-developed composition, identify that character and explain why he or she is heroic.”
• You may receive a prompt that focuses on the use of theme in writing, for example: “In many literary works, the main character goes through some experience that causes him or her to gain insight and change the way he or she is living. The moment of insight is called an epiphany. From a work of literature you have read in or out of school, select one main character who experiences an epiphany and explain how it changes his or her life.”
• A complete list of previous essay prompts for the MCAS essay can be found at http://www.duxbury.k12.ma.us/Page/4853 .

• Each sample essay also contains evaluator comments that explain why the essay received a high score or a low score. For example, an essay that received the highest score, 6, in Topic/Idea development opens with a rich first sentence that frames the rest of the essay, which is on Cheryl Strayed’s autobiographical novel Wild: From Lost to Found on the Pacific Crest Trail . The writer uses the opening analysis of the character’s internal and external battles to discuss how the character develops self awareness and emotional growth in the course of the novel. The writer returns to these themes throughout the five paragraph essay and uses strong examples from the text to support her ideas. The evaluator noted there is “careful selection and development of details” as well as “ language that supports meaning.” [5] X Research source
• In comparison, an essay that received the lowest score, 1, in Topic/Idea development, is only four lines long and provides a very brief response that is minimal but on topic. However, the writer does not demonstrate any awareness of what the essay prompt is asking him to discuss in his essay and he does not present any rich detail, strong development of ideas, or meaningful analysis of the text. [6] X Research source

Creating an Outline

• Often, your MCAS essay will be most effective if you chose one literary work that you have read recently and remember well. You will need to recount the plot and characters of the literary work, as well as any techniques, motifs, or themes used in the work. It will help if you choose a work that you are confident you can recall in detail.

• To save time, you can start with a rough thesis statement and then adjust your thesis statement once you are done your rough draft. Often, you can get a better sense of your thesis statement and the overall goal of the essay once you have finished a rough draft.
• If we use the high scoring essay on Cheryl Strayed as an example, the thesis statement appears at the end of the first paragraph: “Written through the perspective of author Cheryl Strayed, Wild: From Lost to Found on the Pacific Coast Trail illustrates Strayed’s own personal battle through the story of a classic life interrupted, which forces her to contemplate the polar extremes of what one woman can face.” [10] X Research source

• Introduction: Your beginning paragraph should contain an engaging first sentence and your thesis statement. Some writers find it easier to write create a temporary introduction and revise it once they are finished with the essay. This will ensure the introduction is cohesive with the rest of the essay.
• Body paragraph 1-3: Each paragraph should discuss one major point of your thesis, with at least one supporting example.
• Conclusion: This paragraph should summarize your main argument and restate your thesis. You may also want to include last thoughts around the essay question.

Writing the First Draft

• An interesting or surprising example: This could be a personal experience or a key moment in the literary work you are discussing in your essay.
• A provocative quotation: This could be from the literary work you are using for your essay or one that feels relevant to your topic.
• A vivid anecdote: An anecdote is a very short story that carries moral or symbolic weight. Think of an anecdote that might be a poetic or powerful way to start your essay.
• A thought provoking question: Create a question that will get your reader thinking and engaged in your topic.

• Body paragraph 1: Introduce the literary work and provide a brief, engaging synopsis of the book up to the turning point for the main character. For example, the death of Strayed’s mother from cancer and the breaking up of her family leads Strayed to fill her sense of loneliness and depression with a solo journey on the Pacific Coast Trail.
• Body paragraph 2: Discuss how the literary work responds to the essay prompt and give a detailed analysis of the work based on the prompt. In the Strayed essay, the writer uses Strayed’s physical struggles on the gruelling Pacific Coast Trail to discuss the internal battle Strayed is also dealing with as she processes her grief and depression.
• Body paragraph 3: Look at how a climax or pivotal moment to the literary work highlights the technique, motif, or theme noted in the essay prompt. In the Strayed essay, the writer uses the themes of nature and fate in the novel to discuss how the main character comes to terms with her external and internal struggles.

• For example, you may restate your thesis so that is connects to the larger themes of your essay. The essay on Cheryl Strayed’s Wild ends with this restatement: “Cheryl Strayed’s battle did indeed begin in the mind, but unfolded to become an expedition that illustrated her own hardiness in conquering not only her internal conflict but also the unknown situations of fate and nature.” [13] X Research source

Creating a Final Draft

• Remember the guidelines for a high score in Topic/Idea development: demonstrate rich topic/idea development, careful and subtle organization, and use language effectively in your essay. You should also keep in mind the high score for Standard English conventions: demonstrate control of sentence structure, grammar and usage, as well as a strong grasp of complex sentence structure and standard English conventions.

• Always make sure you use proper grammar and spelling in your essay, as you will be deducted marks in the Standard English conventions category if you miss any misspelled words or grammatical errors.

• For example, your essay on Cheryl Strayed’s Wild could be: “A Wild Woman’s Self Discovery” or “A Classic Life Interrupted”.

Expert Q&A

You might also like.

• ↑ http://www.duxbury.k12.ma.us/Page/4853
• ↑ http://www.doe.mass.edu/mcas/student/2014/question.aspx?GradeID=10&SubjectCode=ela&QuestionID=33209#
• ↑ http://www.emcp.com/product_catalog/resourcefile.php?ID=503
• ↑ http://www.doe.mass.edu/mcas/student/2014/answer.aspx?QuestionID=33209&AnswerID=109303
• ↑ http://www.doe.mass.edu/mcas/student/2014/answer.aspx?QuestionID=33209&AnswerID=100363
• ↑ http://www.historytoday.com/elliot-richman/how-write-essay-under-exam-conditions
• ↑ http://writingcenter.unc.edu/handouts/introductions/

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MCAS Resource List Get Epic : * This website is for students to pick just-right books in different genres. There are informational videos on various topics. This website is suitable for all grade levels. Embarc Online : * This webiste is suitable for parents to understand our Eureka Math Curriculum. This webiste is completely aligned with our math program. Exact Path Reading and Math : * This website is suitable for all 2-5 students to take their own path in reading or math. This aligns with our curriculum. Keyboarding Without Tears: * This is a website for students to use to become proficient keyboarders! MCAS Sample Work and Scoring Guide: * Within this link you will find scoring guides and samples of student work for released items from MCAS tests. Scoring guides and student work samples are provided for the following item types: open-response items, constructed-response items, essay questions, and writing prompts. MCAS Released Items: * You can access these English Language Arts, Math, and Science questions for students to practice!

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Practice Test English Language Arts: Grade 7

This practice test english language arts: grade 7 assessment also includes:.

• Paper-Based Answer Key/Scoring Rubric
• Computer-Based Practice Test
• Computer Based Answer Key/Scoring Rubric
• Text-to-Speech Practice Test
• Approved ELA Graphic Organizer: Essay
• Approved ELA Graphic Organizer: Story
• Reading Passage
• Join to access all included materials

Practice makes perfect. A practice test designed for the ELA MCAS Assessment gives seventh grade learners the opportunity to answer reading comprehension questions and respond to essay prompts. Questions involve general fiction and historical nonfiction texts.

Additional Tags

Instructional ideas.

• Go over question formatting, pointing out bold words and other key terms
• Model how to outline and write an essay like those included in the practice test

Classroom Considerations

• Instead of printing out answer sheets, record responses on regular sheets of paper
• Includes questions that require readers to compare and contrast two texts on the same topic
• Offers graphic organizers and computer-based testing to accommodate different learning styles and classroom formats
• Lacks a rubric or sample responses to help assess responses to essay prompts

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MCAS Resources

HERE is a digital version of the ELA MCAS exam. A digital version of the 2019 ELA exam can also be found on THIS page – if you wish to practice the online version, you will need the one reading passage which is not included on this site, which can be found HERE . The 2019 version lacks one feature – the ability to change the size of the two colums when you have a reading passage AND the questions on the same page. The “Next Generation” MCAS ELA exam (2019-Present) includes:

THE TEST IS STILL UNTIMED – You can take as much time as you need

THE ESSAYS HAVE A 5000-CHARACTER MAXIMUM – That is roughly equivalent to two hand-written pages. Our recommendation, of course, is to get as close to that maximum as you can on every essay. Student feedback tells us that 5000 characters felt **really** short to a lot of students.

ANY STUDENT WHO IS, OR EVER HAS BEEN AN ELL STUDENT IS ALLOWED TO USE A WORD-TO-WORD DICTIONARY ON THE EXAM

SYNTHESIS ESSAY WRITING The most common essay prompt is an analytical/explanatory prompt which is closest to most of the writing you have done in your English classes last year and this year. Many of them will ask you to respond to a single prompt, so there’s no need to review how that works. But you will almost certainly also get a synthesis prompt that asks you to respond to two or more texts.

Our suggestion: If the prompt asks you to COMPARE (show similarity) between multiple passages, OR if it asks you to CONTRAST (show disagreement) between two or more passages, you should handle the texts one at a time. If the prompt asks you to COMPARE AND CONTRAST (show similarity AND THEN difference), then begin by showing the similarity, using every text at once, then show difference, again using all of the texts simultaneously. If the prompt doesn’t specify whether you should compare or contrast, you should still choose the organization suggested above. CLICK HERE for our page explaining synthesis structure in better detail.

Also, CLICK HERE to see an Argument prompt from the 2023 MCAS, including several HHS students’ responses

NARRATIVE ESSAY WRITING FOR HELP ON WRITING A NARRATIVE, CLICK HERE *** If you are asked to write a Narrative Essay, READ THE INSTRUCTIONS CAREFULLY! If the prompt tells you you have to write from a character’s perspective, you must write a 1st person narrative. If it tells you to “write a story” and doesn’t specify the POV, you can choose any perspective that you’d like. For example, in the sample essay linked below, the one writing about an abandoned house, one of the better responses writes from the perspective of the house itself*** *** Also, presume that your reader knows the plot of the story/poem/essay that you are responding to. You do not need to spend any time explaining who characters ARE, because your reader will definitely know those plot details***

Sample MCAS Narrative Response

Click HERE for a sample question that asks students to examine a painting and write a creative response. Sample answers are included as well. 

HELPFUL TIPS FOR WRITING AN ARGUMENT ESSAY * While the rules for powerful writing are roughly the same here as they are in an analytical essay, one key difference is that you are allowed, encouraged even, to use first-person pronouns. Don’t overdo it, but it’s acceptable. * Pay attention to the writing prompt – it might tell you exactly who your audience is, and you will want to adjust your response accordingly. If the prompt asks you to write a letter to a U.S. Senator asking for a change, that will sound different than a prompt that asks you to give a speech in from of an auditorium full of excited students. * Your job is to persuade the reader to your side of the argument. Use a variety of persuasive techniques: Logos (fact-driven), Pathos (emotion-driven) and Ethos (expert source). You do not need to handle these one at a time – in fact, moving among these three techniques can give your argument momentum. * If you have a good grasp of Logos/Ethos/Pathos , it is often a good idea to go light on the pathos – it can feel artificial or easy to disagree with. It is, however, often powerful to either begin or end with pathos. * Argument essays will be a response to articles that you read. If you know the prompt ahead of time (like our first TEST HINT below suggests), you can compile your best factual support as you go through the article the first time. CLICK HERE to see an Argument prompt from the 2023 MCAS, including several HHS students’ responses

Literary/Grammar Terms that have appeared on the MCAS since 2006 Irony / Ironic (This shows up pretty commonly) Metaphor Theme Hyperbole Conflict Synonym Myth Imagery Mood Folktale Stanza Symbolism / Symbolize (you can expect a question about symbolism most years) Satire Figurative Language Point of View Contrast Tone  (Beyond this particular wording, the tests almost always ask about the “main attitude” or the “overall feel” of a passage – these questions commonly require you to consider the tone) Ellipsis Personification Line Break (in poetry – i.e. what does the line break suggest?) Sonnet Noun Verb Adjective Adverb (Parts of Speech have become a common question in recent years)

TEST HINT: PREPARE YOUR READING FOCUS IN ADVANCE : A good amount of MCAS questions ask you to focus on a specific paragraph or line of a passage, or perhaps to compare two specific aspects of two different passages. If only you knew this before you started reading. WELL, YOU CAN! A great test strategy is to scan through and read the questions before you read the first line of the first passage . As you go, take notes on one of your scrap papers to tell you which parts of each passage you will need to respond to. Our suggestion: The first thing you’ll see on the test is a reading passage. Write the title on the top of your scrap page. When you click ahead to the next part, you’ll either start getting questions about that passage, or you will get a second reading passage. If it’s a reading passage, write the title on the same line of your page, like you are starting a second column. Then, once you do get to the questions, make CLEAR notes about what the test will ask you. If Question one asks about the main purpose of paragraph 6 of The Glass Castle , I’d add the note “Purpose of Paragraph 6” under where I wrote “The Glass Castle.” If there’s something that asks you about two or more prompts, write that note in a circle in BOTH columns. Proceed through the entire reading section, INCLUDING ANY WRITING PROMPTS CONNECTED TO THAT PASSAGE and then backtrack to the first page and begin reading, but with a plan. TEST HINT: TEXT INTERPRETATION QUESTIONS : Many MCAS questions simply rely on deciphering context, but some, like the tone question, or the poetry line break analysis, require you to interpret something deeper. For questions like these, it’s usually a good idea to guess the answer BEFORE looking at the choices , because some of the wrong answers will be ones that you might be able to make a (faulty) case for. But if you have a pretty decent guess, only one of the four answers will be a close match to it.

The phrasing that ought to trigger this strategy is any time a question asks something like “What is the main reason…” or “What is the purpose of…” or “What does [this word] mean in the context of the sentence…”

TEST HINT: TWO-PART QUESTIONS: A lot of students are initially thrown by the two-part questions, where the second part follows up on the first part. The bad news is that you are unable to get the second part correct if you get the first part wrong. But there is good news! You can use the second set of answers as a hint to help you get BOTH parts right. Think of it this way – the test is asking you to get a PAIR of answers right, so if a question in part A has no corresponding support in part B, then you can throw out the first answer, no matter how appealing it is. Similarly, if you are completely thrown by a question, you can still look into the answers for pairings, to help you eliminate wrong choices. Here is one example:

Question A: Which of these is a food? (A) Strawberry (B) Sock (C) Banana (D) Sand

Wait… this question has two right answers! That’s impossible! Thanks, MCAS. You’re the worst. BUT WAIT!! Check out the next question…

Question B: Based on your answer to question A, what color do you most associate with that food? (A) Blue (B) Black (C) Red (D) Orange

OK, look at how much you can trim down the answer sets… first, there is nothing blue or orange in Question A – those answers cannot be correct, even if you weren’t sure if socks and sand could be considered food.  Furthermore, if you can eliminate “socks” and “sand” as possible foods, then try to pair both remaining answers from Question A up with the answer set for question B. The only PAIRING that works is STRAWBERRY with RED. 

And another sample…

Question A: [imagine that this question is completely confusing, and you don’t really understand what is being asked…]

(A) Deception (B) Panic (C) Confidence (D) Annoyance

Question B: Based on your answer to question A, which quote best supports that idea? (A) “My love is like a red, red rose” (line 18) (B) “And could not hope for help. And no help came.” (line 25) (C) “I wake to sleep and take my waking slow” (line 3) (D) “To strive, to seek, to find, and not to yield” (line 40)

At this point, I’m stuck without any possible answer to part A, but I can look for logical pairings to trim down the pack. This strategy will NOT magically provide the answer, but it will help you make a better guess. If I am not trying to force a connection too hard, I notice in the pairs above that answers B and B in the two parts work pretty well together, as do answers C from part 1 and D from part 2. There isn’t as strong of a pairing for A (Deception) and D (Annoyance) in the second half of the question, so without understanding the question at all, and a question with 16 different possible answer pairings at that, I’ve now given myself a 50/50 chance of getting it right. 

MCAS Writing Rubric

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FREE 7th Grade MCAS Math Practice Test

Welcome to our FREE 7th Grade MCAS Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help your student succeed on the 7th Grade MCAS Math test. Not only does the test closely match what students will see on the real MCAS, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your student’s MCAS Practice test. Your student will have the chance to try out the most common 7th Grade MCAS Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free 7th Grade MCAS Math practice tests and study resources (updated for 2021) to help your students ace the 7th Grade MCAS Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to practice.

The Absolute Best Book to Ace the 7th Grade MCAS Math Test

Mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems, 10 sample 7th grade mcas math practice questions.

1- What is the slope of a line that is perpendicular to the line \(4x-2y=12\)?

2- Simplify: \(5(x-2y)+(2-x)^2 = (5x-10y)+(4-4x+x^2) = x -10y +4 +x^2\) When \(x=3\) and \(y=-2\) ,therefore: \(x -10y +4 +x^2 =3+20+4+9 =36\)

3- The mean of 50 test scores was calculated as 88. However, it turned out that one of the scores was misread as 94 but it was 69. What is the mean?

4- The width of a box is one-third of its length. The height of the box is one-third of its width. If the length of the box is 27 cm, what is the volume of the box?

A. 81 cm\(^3\)

B. 162 cm\(^3\)

C. 243 cm\(^3\)

D. 729 cm\(^3\)

5- In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km, and 55 km. In the next five hours, it travels at an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours.

6- The ratio of boys to girls in a school is 2:3. If there are 600 students in a school, how many boys are in the school.____________

7- The perimeter of the trapezoid below is 54 cm. What is its area? _________

8- In 1999, the average worker’s income increased by $2,000 per year starting from a $24,000 annual salary. Which equation represents income greater than average? (\(I =\) income, \(x = \)number of years after 1999)

A. \(I > 2000 x + 24000\)

B. \(I > -2000 x + 24000\)

C. \(I < -2000 x + 24000\)

D. \(I < 2000 x – 24000\)

9- Which of the following graphs represents the compound inequality?

10- A football team had $20,000 to spend on supplies. The team spent $14,000 on new balls. New sports shoes cost $120 each. Which of the following inequalities represents how many new shoes the team can purchase?

A. \( 120x+14,000 ≤20,000 \)

B. \(120x+14,000 ≥20,000\)

C. \(14,000x+12,0 ≤20,000 \)

D. \( 14,000x+12,0 ≥20,000 \)

11- Two dice are thrown simultaneously, what is the probability of getting a sum of 6 or 9?

A. \(\frac{1}{3}\)

B. \(\frac{1}{4}\)

C. \(\frac{1}{6}\)

D. \(\frac{11}{36}\)

12- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool? __________

13- Which graph corresponds to the following inequalities? \(y≤ x + 4\) \(2x + y ≤ – 4\)

14- A bank is offering \(4.5\%\) simple interest on a savings account. If you deposit $8,000, how much interest will you earn in five years?

15- A card is drawn at random from a standard 52–card deck, what is the probability that the card is of Hearts? (The deck includes 13 of each suit clubs, diamonds, hearts, and spades)

D. \(\frac{1}{52}\)

16- How long does a 420–mile trip take moving at 50 miles per hour (mph)?

B. 6 hours and 24 minutes

C. 8 hours and 24 minutes

D. 8 hours and 30 minutes

17- 11 yards 6 feet and 4 inches equals how many inches?

18- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) – 200 (0.30)\)

C. \((200) (0.15) – (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

19- Which of the following points lies on the line \(2x + 4y = 10\)

A. \((2, 1)\)

B. \((–1, 3)\)

C. \((–2, 2)\)

D. \((2, 2)\)

20- \(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = \)?

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1- A The equation of a line in slope intercept form is: \(y = mx + b\) Solve for \(y\). \(4x-2y=12 ⇒ -2y=12-4x ⇒ y=(12-4x)÷(-2) ⇒ y=2x-6\) The slope of this line is 2. The product of the slopes of two perpendicular lines is\( -1\). Therefore, the slope of a line that is perpendicular to this line is: \(m_1 × m_2 = -1) ⇒ 2 × (m_2) = -1 ⇒ (m_2) = -(\frac{1}{2}\)

2- C Simplify: \(5(x-2y)+(2-x)^2 = (5x-10y)+(4-4x+x^2) = x -10y +4 +x^2\) When \(x=3\) and \(y=-2\) ,therefore: \(x -10y +4 +x^2 =3+20+4+9 =36\)

3- C \(average (mean) = \frac{sum \space of \space terms }{number \space of \space terms}⇒ 88 = \frac{sum \space of \space terms}{50}⇒ sum = 88 × 50 = 4400\) The difference of 94 and 69 is 25. Therefore, 25 should be subtracted from the sum. \(4400 – 25 = 4375\) \(mean =\frac{sum \space of \space terms}{number \space of \space terms}⇒ mean = \frac{4375 }{50}= 87.5\)

4- D If the length of the box is 27, then the width of the box is one-third of it, 9, and the height of the box is 3 (one-third of the width). The volume of the box is: \(V = lwh = (27) (9) (3) = 729\)

5- C Add the first 5 numbers. \(40 + 45 + 50 + 35 + 55 = 225\) To find the distance traveled in the next 5 hours, multiply the average by number of hours. \(Distance = Average × Rate = 50 × 5 = 250\) Add both numbers. \(250 + 225 = 475\)

6- 240 The ratio of boys to girls is 2:3. Therefore, there are 2 boys out of 5 students. To find the answer, first divide the total number of students by 5, then multiply the result by 2. \(600 ÷ 5 = 120 ⇒ 120 × 2 = 240\)

7- 130 The perimeter of the trapezoid is 54 cm. Therefore, the missing side (high) is \(= 54 – 18 – 12 – 14 = 10\) Area of a trapezoid: \( A = \frac{1}{2}h (b_1 + b_2) = \frac{1}{2}(10) (12 + 14) = 130\)

8- A Let \(x\) be the number of years. Therefore, $2,000 per year equals 2000\(x\). starting from $24,000 annual salary means you should add that amount to 2000\(x\). Income more than that is: \(I > 2000x + 24000\)

9- D Solve for \(x\). \(-2≤2x-4<8 \)⇒ (add 4 all sides)\( -2+4≤2x-4+4<8+4 \) \(⇒ 2≤2x<12 \) ⇒ (divide all sides by 2)\( 1≤x<6\) \(x\) is between 1 and 6.

10- A Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase 120 \(x\). The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most. Now, write the inequality: \(120x+14.000 ≤20.000\)

11- B For Sum 6: (1 & 5) and (5 & 1), (2 & 4) and (4 & 2), (3 & 3), so we have 5 options. For sum 9: (3 & 6) and (6 & 3), (4 & 5) and (5 & 4), we have 4 options. To get a sum of 6 or 9 for two dice: \(5+4=9\) Since we have \(6 × 6 = 36\) total options, the probability of getting a sum of 6 and 9 is 9 out of 36 or \(\frac{1}{4}\).

12- 8 Use the formula of rectangle prism volume. \(V = (length) (width) (height) ⇒ 2000 = (25) (10) (height)\) \( ⇒ height = 2000 ÷ 250 = 8\)

13- A For each option, choose a point in the solution part and check it on both inequalities. A. Point \((–4, –4)\) is in the solution section. Let’s check the point in both inequalities. \(–4 ≤ – 4 + 4, \space It \space works\) \(2 (–4) + (–4) ≤ –4 ⇒ – 12 ≤ – 4\) it works (this point works in both) B. Let’s choose this point \((0, 0)\) \(0 ≤ 0 + 4, \space It \space works\) \(2 (0) + (0) ≤ –4, \space \space That’s \space not \space true!\) C. Let’s choose this point \((–5, 0)\) \(0 ≤ –5 + 4, \space That’s \space not \space true!\) D. Let’s choose this point \((0, 5)\) \(5 ≤ 0 + 4, \space That’s \space not \space true!\)

14- C Use a simple interest formula: I=prt (I = interest, p = principal, r = rate, t = time) \(I=(8000)(0.045)(5)=1800\)

15- B The probability of choosing a Hearts is \(\frac{13}{52}=\frac{1}{4}\)

16- C Use distance formula: \(Distance = Rate × time ⇒ 420 = 50 × T\) divide both sides by 50. \(\frac{420}{50} = T ⇒ T = 8.4 \space hours\) Change hours to minutes for the decimal part. \(0.4 \space hours = 0.4 × 60 = 24 \space minutes\)

17- C \(11 × 36 + 6 × 12 + 4 = 472\)

18- D To find the discount, multiply the number by (\(100\% – \)rate of discount). Therefore, for the first discount, we get: \((200) (100\% – 15\%) = (200) (0.85) = 170\) For the next \(15%\) discount: \((200) (0.85) (0.85)\)

19- B Input \((-1, 3)\) in the \(2x + 4y = 10\) formula instead of \(x\) and y. So we have: \( 2(-1) + 4(3) = 10\) \(-2 + 12 = 10\)

20- A Use PEMDAS (order of operation): \(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = 5 + 8 × (–2) – [4 + 110] ÷ 6 = 5 + 8 × (–2) – [114] ÷ 6 = 5 + (–16) – 19 = 5 + (–16) – 19 = –11 – 19 = –30\)

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by: Effortless Math Team about 4 years ago (category: Articles )

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