Practice Questions
Concept Explanation
Mixed algebra combines linear and quadratic equations, identities, inequalities, and word problems in one assessment.
Strategy
- Identify the topic type first — linear, quadratic, or identity.
- Use the shortest valid method for each sub-problem.
- Verify answers by substitution when time permits.
Example
Solve x² − 9 = 0 and 2x + 1 = 7 together: x = 3 from both when seeking common solution — check 3: 9 − 9 = 0 and 7 = 7.
Common Trap
In mixed sets, do not apply a linear method to a quadratic, or vice versa.
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Q1 Easy
What value of x satisfies the linear equation 3x + 4 = 19?
Explanation3x = 15, x = 5. -
Q2 Easy
Which values of x satisfy the equation x² − 16 = 0?
Explanationx = ±4. -
Q3 Easy
What is the expanded form of the product (x + 4)(x − 4)?
ExplanationDifference of squares: x² − 16. -
Q4 Medium
Given that x + y = 10 and xy = 21, what is the value of (x − y)²?
Explanation(x − y)² = 100 − 84 = 16. -
Q5 Easy
Which inequality describes all values of x for which 2x − 3 is greater than 5?
Explanation2x > 8, x > 4. -
Q6 Medium
What is the simplified value of √32 + √18?
Explanation4√2 + 3√2 = 7√2. -
Q7 Medium
For the quadratic equation x² + 3x − 10 = 0, what is the sum of the roots?
ExplanationSum = −3.
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Q8 Easy
One number is 7 more than twice another. If the two numbers are 23 and 8, which expression correctly shows that the larger number equals 7 more than twice the smaller?
Explanation2 × 8 + 7 = 23. -
Q9 Easy
What are the roots of the quadratic equation x² − 5x + 6 = 0?
ExplanationRoots 2 and 3. -
Q10 Medium
If 5x = 125, what is the value of x?
Explanation125 = 5³, so x = 3. -
Q11 Hard
Given the simultaneous equations 4x + 3y = 18 and x + y = 5, what is the value of y?
Explanationx = 3, y = 2. -
Q12 Hard
Find the value of (102)² − (98)².
Explanation(102 + 98)(102 − 98) = 200 × 4 = 800. -
Q13 Medium
The present age of a father is 40 years and that of his son is 10 years. After how many years will the father be twice as old as his son?
Explanation40 + t = 2(10 + t) gives t = 20. -
Q14 Hard
For what value of k does the quadratic equation x² + kx + 9 = 0 have equal roots?
ExplanationD = k² − 36 = 0 gives k = ±6.
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DS1 Easy
What is the positive value of x that satisfies the equation 2x² − 8 = 0?
Statement Ix² = 4.
Statement IIx is positive.
ExplanationNeed both: x = 2. -
DS2 Medium
Two numbers x and y satisfy x − y = 4 and xy = 21. What is the value of x + y?
Statement Ix − y = 4.
Statement IIxy = 21.
ExplanationNeed both to find x, y and sum 10.
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DS3 Medium
What is the value of the algebraic expression (a + b)² − (a − b)²?
Statement Ia = 5.
Statement IIb = 3.
ExplanationNeed both: 4ab = 60. -
DS4 Hard
The quadratic equation x² − 6x + k = 0 has roots 2 and 4. What is the value of k?
Statement ISum of roots is 6.
Statement IIOne root is 2.
ExplanationNeed both: product k = 8.