You’ve finished the course now. But before you go let’s do revision and a final exam!

Revision Points

To do well in your maths (Grade 9 entry) exam, remember: identify type, if can complete quickly, then solve, if not, move on and return with the last resort being, guess.

This will help you move through quickly but also help with getting a higher quantity of questions correct.

Overarching points to remember for each of the checkpoints are:

• Numbers: Rational, Irrational and Decimals – Rational numbers are numbers that can be expressed as a fraction. Irrational numbers cannot e.g. Π A decimal is a number representation 0.123 etc… - terminating fractions have a finite number of digits, recurring decimals have a repeating pattern.
• Index notation - Index notation compactly shows repeated multiplication—e.g., 2³ means 2 × 2 × 2. Key rules include adding exponents when multiplying (2³ × 2² = 2⁵) and subtracting when dividing (2⁵ ÷ 2² = 2³).
• Percentages - Percentages express parts per hundred—e.g., 25% means 25 out of 100 (25/100 = 0.25). They let you convert easily between fractions and decimals and solve problems like a 20% discount on $150, which saves $30.
• Rates, Ratios and Distance-Time Problems - Ratios compare quantities—e.g., 3:2 means 3 parts to 2 parts (5 parts total) and can be simplified using their greatest common divisor. Rates are similar but compare different units (like $2 per 100g or 50 km/h), and distance–time problems use formulas like distance = speed × time.
• Money Maths - Money maths uses basic arithmetic to calculate cost price (CP), selling price (SP), profit/loss, and discounts. For example, profit = SP – CP and profit/loss percentages are based on CP. Discounts reduce the marked price, ensuring accurate final sale values.
• Algebra- Simplify & Extend - Algebra uses symbols to solve problems. For example, in 2x + 5y – 7, 2 and 5 are coefficients, x and y are variables, and –7 is a constant (three terms total). Distribute and combine like terms—e.g., 3(2x – 4y + 5) simplifies to 3x – 25y + 24—to make expressions easier to work with.
• Algebra – Factorise & Problem Solving - Factorisation splits expressions into factors using the GCF (General Common Factor). For instance, 6x + 9y factors to 3(2x + 3y) because 3 divides both 6 and 9. Algorithms guide problem-solving, and error detection (e.g., substituting x = 1, y = 1) checks work.
• Graphs: Linear - The Cartesian plane is a 2D coordinate system with x‑ and y‑axes that divide the plane into quadrants; for example, (3,2) is 3 right, 2 up. Linear equations like y = 2x + 1 graph as straight lines with slope 2 and y‑intercept 1.
• Graphs: Non-Linear - Non-linear relationships produce curved graphs and lack a constant rate of change. Examples: area = side² (quadratic), population = 2^t (exponential), and time = 100/speed (reciprocal). We interpret steepness, maxima, and curvature to understand real-world scenarios and make predictions.
• Time and Duration - 12-hour time uses a.m./p.m. (e.g., 3:00 p.m.), whereas 24-hour time ranges from 00:00 to 23:59 (e.g., 15:00). Convert times by adding 12 for p.m., or subtracting 12 in 24-hour format. Adding durations (2:40 + 1:30 = 4:10) finds start/end times.
• Circles – A circle’s radius r extends from its centre to its edge, and its diameter d=2r. The circumference equals C=πd (or 2πr), and the area is A=πr². For example, if r=7, then C=44 cm and A=154 cm² (π=22/7).
• Congruency and Angle Properties - Congruent shapes have exactly matching sides and angles (e.g., two squares). Transformations (translation, rotation, reflection) preserve congruence. Triangles are congruent if they satisfy SSS, SAS, ASA, or RHS. Quadrilaterals have interior angles summing to 360° while triangles have interior angles summing to 180°; parallelograms have opposite sides equal, proven using congruent triangles.
• Units of Measurement, Perimeter & Area - Measurement uses standard units (e.g., 1 m = 100 cm, 1 m² = 10 000 cm², 1 L = 1000 cm³) to calculate perimeter and area of shapes. Rectangles and parallelograms use base × height, trapeziums use 1⁄2(a + b)h, and rhombus/kite areas are 1⁄2(d₁ × d₂). Understanding conversions (e.g., 1 ha = 10 000 m²) and applying correct formulas solves practical geometry problems.
• Volume - Prisms have a constant cross-section; their volumes are found by (area of cross-section) × (length). For example, a rectangular prism with dimensions 3 × 4 × 5 has volume 60 cm³, and a triangular prism’s volume is 1⁄2bh × length.
• Chance - Probability relies on complementary events (P(A) + P(not A) = 1) and formulas like P(A ∪ B) = P(A) + P(B) − P(A ∩ B). "At least k" means k or more, and mutually exclusive events simply add their probabilities. Two-way tables and Venn diagrams organize outcomes, showing overlaps (like P(A ∩ B)) or separate regions (A ∖ B, B ∖ A).
• Data - Statistics uses samples to infer about entire populations. Key measures include mean (e.g., (2+3+7)/3=4), median (the middle value), and range (max-min). Outliers can distort these measures. Larger samples produce more stable estimates and further improve accuracy for deeper population insights.

Final Exam

The final exam is a printable PDF.

Now, download, print and complete this exam (Your time limit: 30 minutes. Number of questions: 60).

Click here to Download the Mathematical Reasoning Exam

When you’re done, download the worded suggested solutions and watch the solutions video with explanations (scroll down to see suggested solutions videos).

Click here to Download the Mathematical Reasoning Exam with Suggested Solutions

It’s been a journey and well done and congratulations!

We wish you all the best for your upcoming exam and will be cheering you on!!

If you have news you’d like to share – we would love to hear about it, get in touch anytime at success@examsuccess.com.au.

Suggested Solutions Videos

For questions 1 through to 10:

For questions 11 through to 20:

For questions 21 through to 30:

For questions 31 through to 40:

For questions 41 through to 50:

For questions 51 through to 60: