Year 9 Maths practice questions

Lock in’s Year 9 Maths course has 7 units with 121 flashcards and 127 practice questions, plus timed exams built fresh each time.

• Indices and algebraic techniquesExpanding brackets; Factorising; Index laws; Zero and negative indices; Scientific notation and significant figures
• EquationsOne- and two-step equations; Brackets and pronumerals on both sides; Equations with fractions; Simple quadratic equations; Formulas: substitution and changing the subject; Worded problems
• Linear relationshipsDistance between two points; Midpoint; Gradient; Gradient-intercept form y = mx + c; Graphing lines and intercepts; Parallel and perpendicular lines; Finding the equation of a line
• Financial mathematicsWages and salaries; Overtime, penalty rates, commission and piecework; Leave loading and net pay; Simple interest; Compound interest; Depreciation
• Pythagoras, trigonometry and geometryCongruent triangles; Similar figures; Pythagoras’ theorem; The trigonometric ratios; Finding unknown sides; Finding unknown angles; Angles of elevation and depression; Bearings
• Area, surface area and volumeUnits of area, volume and capacity; Area of plane and composite shapes; Surface area of prisms; Surface area of cylinders; Volume and capacity of prisms and cylinders
• Statistics and probabilityCollecting and displaying data; Mean, median, mode and range; Quartiles, interquartile range and box plots; Shape of data and comparing data sets; Bivariate data and scatter plots; Probability basics; Two-step experiments; Venn diagrams and two-way tables

Try each question before you open the answer. Written answers show what a full-marks response needs to include.

1. Question 1. Indices and algebraic techniquesMultiple choice

   Simplify y^⁵ × y^⁴

   1. Ay^⁹
   2. By^¹
   3. C2y^⁹
   4. Dy^²⁰
   Show answer

   A. y^⁹

   Add the indices.

2. Question 2. EquationsMultiple choice

   Solve 2x + 9 = 1

   1. Ax = 5
   2. Bx = 4
   3. Cx = −5
   4. Dx = −4
   Show answer

   D. x = −4

   2x = −8.

3. Question 3. Equations: simple quadratic equations2 marks

   Solve x^² − 2x − 24 = 0 and check one of your solutions.

   Show model answer and marking criteria

   Model answer. x^² − 2x − 24 = (x − 6)(x + 4) = 0, so x = 6 or x = −4. Check x = 6: 36 − 12 − 24 = 0 ✓.

   A full-marks answer:

   • Factorises: (x − 6)(x + 4) = 0
   • Solutions x = 6 or x = −4 with a check, e.g. 36 − 12 − 24 = 0
4. Question 4. Linear relationshipsMultiple choice

   The gradient of y = 7 − 2x is…

   1. A−7
   2. B−2
   3. C7
   4. D2
   Show answer

   B. −2

   Rewrite as y = −2x + 7.

5. Question 5. Linear relationships: finding the equation of a line3 marks

   Find the equation of the line through (−2, 7) and (4, −5) in the form y = mx + c.

   Show model answer and marking criteria

   Model answer. m = (−5 − 7)/(4 + 2) = −12/6 = −2. Using (−2, 7): 7 = −2(−2) + c, so 7 = 4 + c and c = 3. The equation is y = −2x + 3.

   A full-marks answer:

   • Gradient m = (−5 − 7)/(4 − (−2)) = −12/6 = −2
   • Substitutes a point: 7 = −2(−2) + c, so c = 3
   • Equation y = −2x + 3
6. Question 6. Financial mathematicsMultiple choice

   An annual salary of $78 000 paid monthly gives…

   1. A$6500
   2. B$3000
   3. C$1500
   4. D$7800
   Show answer

   A. $6500

   78 000 ÷ 12.

Write every line of working, not just the answer. Most marks in a Maths exam are for method, so a correct final number with no working can lose marks, and a small slip with clear working usually keeps most of them. When you get one wrong, redo it from a blank page a day later.

In Lock in, every Maths topic has short notes, then flashcards that use spaced repetition: rate each card Again, Hard, Good or Easy and it comes back just before you would forget it. Practice questions come in three levels, Foundation, Standard and Complex. Three right in a row moves you up a level, and two wrong moves you back.

Press Study for me and the app builds a 15 to 20 minute session from the cards that are due, the mistakes that are due and questions on your weakest topics. Anything you get wrong comes back 1, 3 and 7 days later until you get it right. When an exam is close, sit a timed practice exam with AI marking.

More Year 9 subjects

Year 9 English practice questions, Year 9 Science practice questions, Year 9 History practice questions, Year 9 Geography practice questions, Year 9 PDHPE practice questions.

Maths in other years

Year 7 Maths practice questions, Year 8 Maths practice questions, Year 10 Maths practice questions.