Gr. 10 Mathemats
Term 2 - 2024
Paper 1
Total: 85 marks Time: 1 ½ hours
Learner’s name: ____________________________________ Gr. 10: ___________.
Instructions and information:
• This question paper consists of two questions, answer both questions.
• The use of a calculator is not allowed.
• No Tip – Ex may be used.
• Show all the steps that were required in order to get to the answer.
• Good luck!!
Topics covered in this test:
Rational expressions:
• Identifying undefined and real values.
• Simplifying expressions.
• Factoring expressions.
Algebraic equations and formulas:
1|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
, • Solving quadratic equations.
• Rearranging formulas to make a specific variable the subject.
• Solving inequalities.
• Solving systems of equations.
• Formulating and solving word problems involving equations.
Number patterns:
• Identifying terms in a sequence.
• Finding the nth term of a sequence.
• Calculating the sum of terms in a sequence.
Functions and graphs:
• Understanding the behavior of functions.
• Graphing functions.
• Finding intersections of functions.
• Determining equations of functions.
• Analyzing ranges and symmetries of functions.
Transformation of functions:
• Reflecting functions along axes.
• Identifying asymptotes.
• Sketching graphs of functions.
• Finding intersections of functions.
2|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
, QUESTION 1
𝑥 2 −1
1.1 Given the expression : . For whcih values of 𝑥 will be 𝑃 be:
𝑥−2
1.1.1 Undefined (1)
1.1.2 Real (2)
1.2 Simplify the following expressions fully. Leave your answer in a positive exponent
where necessary
1
1.2.1 (3𝑎)2 × 9𝑎 (2)
3
√𝑎 1 1
𝑏
1.2.2 -𝑎+𝑏 (2)
√𝑎𝑏
1.3 Factorise the following expressions fully:
1.3.1 𝑥 2 + 6𝑥 + 9 (2)
1.3.2 9𝑎2 + 12𝑎𝑏 + 4𝑏 2 (3)
1.3.3 𝑥 3 + 64 (2)
[14]
QUESTION 2
2.1 Solve for 𝑥
2.1.1 𝑥 2 + 8𝑥 = 15 (3)
2
2.2 Given 𝐴 = 𝜋 (𝑟 2 + 𝑠 2 ). Make 𝑠 the subject of the formula. (5)
3
2.3 Solve for 𝑥 if √2 (4𝑥 3 − 9) ≥ 3 (3)
2.4 Solve the following equations simultaneously for 𝑎 and 𝑏:
2𝑎 + 3𝑏 = 1 and 4𝑎 − 𝑏 = 7 (5)
2.5 Marcus is 5 years older than twice his sister is at the moment. In 10 years time,
Marcus will be three times as old as his sister. Formulate and solve an
equation to find his sisters current age. (5)
[21]
3|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
Term 2 - 2024
Paper 1
Total: 85 marks Time: 1 ½ hours
Learner’s name: ____________________________________ Gr. 10: ___________.
Instructions and information:
• This question paper consists of two questions, answer both questions.
• The use of a calculator is not allowed.
• No Tip – Ex may be used.
• Show all the steps that were required in order to get to the answer.
• Good luck!!
Topics covered in this test:
Rational expressions:
• Identifying undefined and real values.
• Simplifying expressions.
• Factoring expressions.
Algebraic equations and formulas:
1|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
, • Solving quadratic equations.
• Rearranging formulas to make a specific variable the subject.
• Solving inequalities.
• Solving systems of equations.
• Formulating and solving word problems involving equations.
Number patterns:
• Identifying terms in a sequence.
• Finding the nth term of a sequence.
• Calculating the sum of terms in a sequence.
Functions and graphs:
• Understanding the behavior of functions.
• Graphing functions.
• Finding intersections of functions.
• Determining equations of functions.
• Analyzing ranges and symmetries of functions.
Transformation of functions:
• Reflecting functions along axes.
• Identifying asymptotes.
• Sketching graphs of functions.
• Finding intersections of functions.
2|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
, QUESTION 1
𝑥 2 −1
1.1 Given the expression : . For whcih values of 𝑥 will be 𝑃 be:
𝑥−2
1.1.1 Undefined (1)
1.1.2 Real (2)
1.2 Simplify the following expressions fully. Leave your answer in a positive exponent
where necessary
1
1.2.1 (3𝑎)2 × 9𝑎 (2)
3
√𝑎 1 1
𝑏
1.2.2 -𝑎+𝑏 (2)
√𝑎𝑏
1.3 Factorise the following expressions fully:
1.3.1 𝑥 2 + 6𝑥 + 9 (2)
1.3.2 9𝑎2 + 12𝑎𝑏 + 4𝑏 2 (3)
1.3.3 𝑥 3 + 64 (2)
[14]
QUESTION 2
2.1 Solve for 𝑥
2.1.1 𝑥 2 + 8𝑥 = 15 (3)
2
2.2 Given 𝐴 = 𝜋 (𝑟 2 + 𝑠 2 ). Make 𝑠 the subject of the formula. (5)
3
2.3 Solve for 𝑥 if √2 (4𝑥 3 − 9) ≥ 3 (3)
2.4 Solve the following equations simultaneously for 𝑎 and 𝑏:
2𝑎 + 3𝑏 = 1 and 4𝑎 − 𝑏 = 7 (5)
2.5 Marcus is 5 years older than twice his sister is at the moment. In 10 years time,
Marcus will be three times as old as his sister. Formulate and solve an
equation to find his sisters current age. (5)
[21]
3|Page www.summariessa.co.za Mathematics
Grade 10 June Paper 1
