10 Most Common 7th Grade IAR Math Questions

B. \(8\)

C. \(18\)

D. \(45\)

4- If \(x=- 8\), which equation is true?

A. \( x(2x-4)=120\)

B. \(8 (4-x)=96\)

C.\( 2 (4x+6)=79\)

D. \( 6x-2=-46\)

5- In a bag of small balls \(\frac{1}{3}\) are black, \(\frac{1}{6}\) are white, \(\frac{1}{4}\) are red and the remaining \(12\) blue. How many balls are white?

A. \(8\)

B. \(12\)

C. \(16\)

D. \(24\)

6- A boat sails \(40\) miles south and then \(30\) miles east. How far is the boat from its start point?

A. \(45\)

B. \(50\)

C. \(60\)

D. \(70\)

7- Sophia purchased a sofa for \($530.40\). The sofa is regularly priced at \($624\). What was the percent discount Sophia received on the sofa?

A. \(12\%\)

B. \(15\%\)

C. \(20\%\)

D. \(25\%\)

8- The score of Emma was half that of Ava and score of Mia was twice that of Ava. If the score of Mia was \(60\), what is the score of Emma?

A. \(12\)

B. \(15\)

C. \(20\)

D. \(30\)

9- A bag contains \(18\) balls: two green, five black, eight blue, a brown, a red, and one white. If \(17\) balls are removed from the bag at random, what is the probability that a brown ball has been removed?

A. \(\frac{1}{9}\)

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

C. \(\frac{16}{17}\)

D. \(\frac{17}{18}\)

10- A rope weighs \(600\) grams per meter of length. What is the weight in kilograms of \(12.2\) meters of this rope? (\(1\) kilograms \(= 1,000\) grams)

A. \(0.0732\)

B. \(0.732\)

C. \(7.32\)

D. \(7,320\)

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Answers:

2- C
Three times \(24,000\) is \(72,000\). One-sixth of them canceled their tickets.
One sixth of \(72,000\) equals \(12,000\) \((\frac{1}{6}) × 72,000 = 12,000\).
\(60,000\) \((72,000 – 12,000 = 60,000)\) fans are attending this week

3- A
It needed to have a ratio to find the value of \(x\).
\(\frac{45}{40}=\frac{2x+4}{16}⇒ 40(2x+4)=45×16 ⇒ x=7\)

4- B
\(8 (4-(-8))=96\)

5- A
\(\frac{1}{3}x + \frac{1}{6}x + \frac{1}{4}x + 12= x\)
\((\frac{1}{3} + \frac{1}{6} + \frac{1}{4}) x+ 12= x\)
\((\frac{9}{12})x+ 12 = x\)
\(x = 48\)
In a bag of small balls \(\frac{1}{6}\) are white then: \(\frac{48}{6} = 8\)

6- B
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(40^2 + 30^2 = c^2 ⇒ 1,600 + 900 = c^2 ⇒ 2,500 = c^2 ⇒ c = 50\)

7- B
The question is this: \(530.40\) is what percent of \(624\)?
Use the percent formula:
\(part = \frac{percent}{100}× whole\)
\(530.40= \frac{percent}{100}× 624 ⇒ 530.40 = \frac{percent ×624}{100}⇒53,040 = percent ×624\)
\(⇒percent = \frac{53,040}{624}= 85\)
\(530.40\) is \(85 \%\) of \(624\). Therefore, the discount is: \(100\% – 85\% = 15\%\)

8- B
If the score of Mia was \(60\), therefore the score of Ava is \(30\). Since the score of Emma was half as that of Ava, therefore, the score of Emma is \(15\).

9- D
If \(17\) balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is \(1\) out of \(18\). Therefore, the probability of not choosing a brown ball is \(17\) out of \(18\) and the probability of having not a brown ball after removing \(17\) balls is the same.

10- C
The weight of \(12.2\) meters of this rope is: \(12.2 × 600 \space g = 7,320 \space g\)
\(1\space kg = 1,000 \space g\) therefore,
\( 7,320 \space g ÷ 1,000 = 7.32 \space kg\)

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