# 10 Most Common 7th Grade IAR Math Questions

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## 10 Sample 7th Grade IAR Math Practice Questions

1- What is the median of these numbers? $$2, 28, 28, 19, 67, 44, 35$$

A. $$19$$

B. $$28$$

C. $$44$$

D. $$35$$

2- Last week $$24,000$$ fans attended a football match. This week three times as many bought tickets, but one-sixth of them canceled their tickets. How many are attending this week?

A. $$48,000$$

B. $$54,000$$

C. $$60,000$$

D. $$72,000$$

3- The following trapezoids are similar. What is the value of $$x$$?

A. $$7$$

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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1- B
Write the numbers in order:
$$2, 19, 28, 28, 35, 44, 67$$
Since we have $$7$$ numbers ($$7$$ is odd), then the median is the number in the middle, which is $$28$$.

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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