Grade 11 Maths Practice Paper 1

Topics covered

• Quadratic equations, formula and inequalities
• Simultaneous equations
• Nature of roots
• Rational exponents
• Quadratic number patterns
• Parabola and hyperbola
• Depreciation and effective rates
• Independent events

Questions with worked answers

• Question 1.1: Equations (3 marks). Solve for x: x(x − 4) = 5
• Question 1.2: Equations (4 marks). Solve, correct to two decimal places: 3x² + 2x − 7 = 0
• Question 1.3: Inequalities (4 marks). Solve: x² + x − 6 ≥ 0
• Question 1.4: Simultaneous equations (6 marks). Solve simultaneously: y − 2x = 1 and x² + y² = 13
• Question 2: Nature of roots (3 marks). Without solving, describe the nature of the roots of 2x² − 3x + 5 = 0.
• Question 3: Exponents (3 marks). Simplify without a calculator: 27^(2/3) × 9^(−1/2)
• Question 4: Number patterns (6 marks). Given the quadratic pattern 3; 6; 11; 18; … (a) Find Tₙ. (b) Find T₂₀. (c) Which term equals 627?
• Question 5: Functions (6 marks). f(x) = −(x − 1)² + 4. Find the turning point, the intercepts and the range of f.
• Question 6: Functions (4 marks). g(x) = 2/(x + 1) − 3. Write down the asymptotes and find the x-intercept.
• Question 7: Finance (3 marks). A car bought for R180 000 depreciates at 18% p.a. on the reducing balance. Find its value after 4 years.
• Question 8: Finance (3 marks). Find the effective annual interest rate equivalent to 9% p.a. compounded monthly.

How to use this paper

• Write down a, b and c before using the quadratic formula.
• Sketch a parabola for every quadratic inequality.
• Round only the final answer, as instructed.

Frequently asked questions

Is this an official Grade 11 paper?

No. It is a Snap&Learn practice paper in the style of a CAPS Grade 11 Paper 1. Official November common papers are linked on the Grade 11 papers page.

Can I use the information sheet?

Yes. In the real exam the quadratic formula and finance formulas are on the information sheet; use it here too.