Sample Questions from Test 19

The first two questions of this mock test (same order and wording as the timed exam).

Mathematical Reasoning

Maya writes each letter of the word LETTER on a separate card.

Question 1 · Multiple choice

Question

Maya writes each letter of the word LETTER on a separate card. Noah writes each letter of the word TREE on a separate card. Maya and Noah each pick one of their own cards at random.

Options

\frac{1}{4}

A. $none of them$
B. $statement 1 only$
C. $statement 2 only$
D. $statement 3 only$
E. $statements 2 and 3 only$

Correct answer

D.

statement 3 only

Explanation

Step 1 — Count the letters in each word LETTER: L, E, T, T, E, R \to 6 cards total Letter Count Probability L 1 1/6 E 2 2/6 = 1/3 T 2 2/6 = 1/3 R 1 1/6 TREE: T, R, E, E \to 4 cards total Letter Count Probability T 1 1/4 R 1 1/4 E 2 2/4 = 1/2 Step 2 — Check Statement 1 "P(Maya picks E) = 1/4" Maya has 2 E's in 6 cards: P(E) = 2/6 = 1/3, not 1/4. Statement 1 is FALSE ✗ Step 3 — Check Statement 2 "P(Maya picks R) = P(Noah picks R)" Maya (LETTER): P(R) = 1/6 Noah (TREE): P(R) = 1/4 1/6 \neq 1/4 \to Statement 2 is FALSE ✗ Step 4 — Check Statement 3 "P(Noah picks E) > P(Maya picks E)" Noah (TREE): P(E) = 2/4 = 1/2 Maya (LETTER): P(E) = 2/6 = 1/3 Is 1/2 > 1/3? Yes! \to Statement 3 is TRUE ✓ Answer: statement 3 only Why Statement 3 is true even though both words contain 2 E's Both LETTER and TREE have exactly 2 E's — but LETTER has 6 cards total while TREE has only 4. Fewer total cards means each card (including E) has a higher probability of being picked. Repeatable method For each statement: P(letter) = (number of that letter) \div (total letters in word). Do NOT just count the number of matching letters — you must divide by the TOTAL.

Mathematical Reasoning

A teacher surveys students on how many books they read in a month.

Question 2 · Multiple choice

Question

A teacher surveys students on how many books they read in a month. The table shows her results. Number of books read Number of students 0318253442

Options

What is the total number of books read by all these students?

A. $10$
B. $22$
C. $38$
D. $44$
E. $50$

Correct answer

C.

38

Explanation

Step 1 — Understand what the table means Each row tells you: "this many students read this many books." 3 students read 0 books: contribute 0 \times 3 = 0 books total 8 students read 1 book each: contribute 1 \times 8 = 8 books total And so on. Step 2 — Calculate the contribution from each row Books read Students Total books (books \times students) 03 0 \times 3 = 0 18 1 \times 8 = 8 25 2 \times 5 = 10 34 3 \times 4 = 12 42 4 \times 2 = 8 Step 3 — Add the totals 0 + 8 + 10 + 12 + 8 = 38 books Answer: 38 Common traps 10 : adding the "books read" column (0+1+2+3+4=10) — this ignores HOW MANY students read each amount. 22 : total number of STUDENTS (3+8+5+4+2=22) — the question asks for total BOOKS, not total people. Repeatable method for frequency tables Total = Σ (value \times frequency) for each row. Always multiply before adding — never just add the values.

Prepare with Precision

Sharpen accuracy on multi-step and diagram-based items.
Get comfortable with the Janison-style interface.
Identify topics to revisit before exam day.

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Books read	Students	Total books (books × students)
0	3	0 × 3 = 0
1	8	1 × 8 = 8
2	5	2 × 5 = 10
3	4	3 × 4 = 12
4	2	4 × 2 = 8

Mathematical Reasoning Mock Test 19: 2027 NSW Selective Format

Skills Covered in this Test

Sample Questions from Test 19

Core Competencies

Prepare with Precision