ICAS Mathematics Number and Algebra — Questions and Answers
Question 1: A number pattern starts 3, 7, 11, 15, ... What is the 10th term of the pattern?
- 37
- 39 (Correct answer)
- 41
- 43
Correct answer: 39
The pattern adds 4 each time, so the 10th term is 3 + 9 × 4 = 39.
Each term increases by 4, so this is an arithmetic pattern with first term 3 and common difference 4. To reach the 10th term you make 9 jumps of 4 from the first term. That gives 3 + 36 = 39. Listing the terms confirms it: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39.
Question 2: Which of the following fractions is closest in value to 0.4?
- 1/3
- 3/8
- 2/5 (Correct answer)
- 3/7
Correct answer: 2/5
2/5 equals exactly 0.4, so it is the closest.
Converting each option gives 1/3 ≈ 0.333, 3/8 = 0.375, 2/5 = 0.4 and 3/7 ≈ 0.429. Since 2/5 is exactly 0.4, it is closest with a difference of zero. ICAS often tests whether students can move between fractions and decimals quickly.
Question 3: Mia buys 3 pens and 2 notebooks for $11. A pen costs $1.50. How much does one notebook cost?
- $2.75
- $3.00
- $3.25 (Correct answer)
- $3.50
Correct answer: $3.25
Three pens cost $4.50, leaving $6.50 for two notebooks, so each notebook is $3.25.
Three pens at $1.50 each cost 3 × 1.50 = $4.50. Subtracting this from the total gives 11 − 4.50 = $6.50 for the two notebooks. Dividing by 2 gives $3.25 per notebook. This is a two-step problem that can also be written as the equation 4.5 + 2n = 11.
Question 4: If 4n − 7 = 25, what is the value of 2n + 1?
- 8
- 15
- 17 (Correct answer)
- 33
Correct answer: 17
Solving gives n = 8, so 2n + 1 = 17.
Add 7 to both sides to get 4n = 32, then divide by 4 to find n = 8. Substituting into 2n + 1 gives 2 × 8 + 1 = 17. A common trap is to stop at n = 8 and choose that as the answer, so always read what the question actually asks for.
Question 5: What is the lowest common multiple (LCM) of 6, 8 and 12?
- 12
- 24 (Correct answer)
- 48
- 96
Correct answer: 24
24 is the smallest number that 6, 8 and 12 all divide into evenly.
Multiples of 12 are 12, 24, 36, 48, ... The number 12 is not divisible by 8, but 24 is divisible by 6 (24 ÷ 6 = 4), by 8 (24 ÷ 8 = 3) and by 12 (24 ÷ 12 = 2). Since 24 is the first multiple of 12 that works, it is the LCM. Options like 48 and 96 are common multiples but not the lowest.
Question 6: A rectangle's length is 3 cm more than its width. If its perimeter is 26 cm, what is its width?
- 5 cm (Correct answer)
- 6 cm
- 7 cm
- 8 cm
Correct answer: 5 cm
Let width = w, then 2(w + w + 3) = 26 gives w = 5.
If the width is w, the length is w + 3. The perimeter is 2(w + w + 3) = 2(2w + 3) = 4w + 6. Setting 4w + 6 = 26 gives 4w = 20, so w = 5 cm. Checking: width 5, length 8, perimeter 2(5 + 8) = 26 cm.
ICAS Mathematics Number and Algebra
A number pattern starts 3, 7, 11, 15, ...
What is the 10th term of the pattern?