Grade 10 is the start of the FET phase, and these skills return in every paper until Matric. Use these questions to prepare for a test or your November exam: try each one first, then compare your working.
Question 1: Quadratic equation
Solve x² + 2x − 15 = 0. Factorise: (x + 5)(x − 3) = 0. Answer: x = −5 or x = 3.
Question 2: Exponential equation
Solve 2ˣ⁺¹ = 16. Write 16 as 2⁴, then equate the exponents: x + 1 = 4. Answer: x = 3.
Question 3: Simultaneous equations
Solve x + y = 5 and x − y = 1. Add the equations: 2x = 6, so x = 3. Substitute to get y. Answer: x = 3 and y = 2.
Question 4: Parabola
For y = x² − 4, find the turning point and x-intercepts. The graph is y = x² moved 4 units down, so the turning point is (0; −4). Set y = 0: x² = 4. Answer: turning point (0; −4) and x-intercepts at x = −2 and x = 2.
Question 5: Trigonometry
Solve sin θ = 0.5 for an acute angle θ. Use the special angles or sin⁻¹ on your calculator. Answer: θ = 30°.
Question 6: Simple interest
R1 000 is invested at 8% simple interest for 3 years. Find the final amount. A = P(1 + in) = 1 000(1 + 0.08 × 3). Answer: R1 240.
Question 7: Distance between two points
Find the distance between A(1; 2) and B(4; 6). d = √[(4 − 1)² + (6 − 2)²] = √(9 + 16) = √25. Answer: 5 units.
Question 8: Midpoint
Find the midpoint of the line joining (2; 3) and (6; 7). Add the x-values and divide by 2, then do the same with the y-values: ((2 + 6)/2; (3 + 7)/2). Answer: (4; 5).
When you get stuck
Set your grade to Grade 10 in Snap&Learn and snap the question. You'll see each step at your grade's level, with the marks a memo would award. Your first three AI solutions are free.