Advanced level 2025 South West Regional Mock TVE mathematics 1

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1. The exact value of sin15∘ is A. 41​(6​+2​) B. 41​(2​+2​) C. 41​(3​+1) D. 41​(6​−2​)

2. Given that $x=2+3\sin t$, and $y=3+2\cos t$, then the Cartesian equation of the curve is A. 9(x−2)2+4(y−3)2=36 B. 4(x−3)2+9(y−2)2=36 C. $3x-2y=13$ D. $3x+2y=12$

3. For what value of $x$, is 23x=0.25? A. 32​ B. −32​ C. −23​ D. 121​

4. The limit of x2−44x−8​ as $x$ tends to 2 is A. $-\infty$ B. 0 C. 41​ D. 8

5. Given that p(x)=x3−3x2+9x+13, the value of $p(-1)$ is A. 2 B. 18 C. 0 D. 6

6. The total number of cartons of square tiles of dimension 30cm by 30cm required to completely cover the floor of a room 3m by 4m is (consider that each carton contains 15 tiles) A. 9 B. 10 C. 11 D. 12

7. The real valued function $f$ is defined on $\mathbb{R}$. The set of real numbers by $f:x\mapsto ax+b$. Given that f−1(4)=5,f−1(2)=3 it implies that the value of $a+b$ is A. 8 B. 1 C. 2 D. 0

8. Given the function f(x)=⎩” />⎨” />⎧​2x+1,7−x,x,​0≤x≤22<x<44≤x≤6​ The function $f$ is continuous at $x$ equals A. 4 B. 5 C. 6 D. 2

9. The area of the finite region bounded by the curve $y=x(2-x)$ and the $x$-axis is A. 34​ square units B. 32​ square units C. 38​ square units D. 316​ square units

10. The set of value of $x$ for which x2−5x+4≤0 is A. $1\le x\le 4$ B. $x\ge 4$ C. $x\in [1,4]$ D. $x\in ]-\infty ,1]\cup [4,+\infty [$

11. limx→4​x−4x​−2​ is A. 0 B. 41​ C. 1 D. 21​

12. A curve is defined such that y2+x2+2y=2. The gradient of the curve at $P(2,-1)$ is A. 38​ B. −38​ C. −83​ D. 83​