Class IX Maths SA-1: Number Systems, Polynomials, Coordinate Geometry, Linear Equations & Lines and Angles: 60 flashcards
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1. What is the definition of a rational number?
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A number that can be written as $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
2. How can you tell if a decimal is irrational?
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Its decimal expansion is non-terminating and non-repeating.
3. How many rational numbers lie between any two rational numbers?
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Infinitely many.
4. What is the coefficient of $x$ in $9x^2 + 4x - 6$?
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$4$
5. What is the standard form of a quadratic polynomial?
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$ax^2 + bx + c$, where $a \ne 0$.
6. Why is $ax^{-2} + bx + c$ not a polynomial?
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Because it contains a negative exponent, and polynomial exponents must be non-negative integers.
7. If the $y$-coordinate of a point is $0$, where does the point lie?
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On the $x$-axis.
8. What is the standard form of a linear equation in two variables?
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$ax + by + c = 0$
9. What do angles in a linear pair add up to?
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$180^\circ$
10. What is an angular bisector?
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A ray that divides an angle into two equal angles.
11. What are perpendicular lines?
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Lines that intersect at $90^\circ$.
12. What are collinear points?
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Points that lie on the same straight line.
13. Factorise $y^2 - 5y + 6$.
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$(y - 2)(y - 3)$
14. State the Factor Theorem.
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If $(x - a)$ is a factor of $P(x)$, then $P(a) = 0$.
15. What are the quadrant signs for Quadrant II?
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$(-, +)$
16. How do you rationalise the denominator of $\frac{1}{7+3\sqrt{2}}$?
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Multiply numerator and denominator by the conjugate $7-3\sqrt{2}$.
17. If $x + y + z = 0$, what is $x^3 + y^3 + z^3$?
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$3xyz$
18. When a transversal cuts parallel lines, what is true about corresponding angles?
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They are equal.
19. When a transversal cuts parallel lines, what do co-interior angles add up to?
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$180^\circ$
20. What is the decimal expansion of $\frac{1}{11}$?
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$0.\overline{09}$ (repeating)
21. Is $\frac{36}{100}$ a terminating or repeating decimal?
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Terminating ($0.36$).
22. What is the degree of a linear polynomial?
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$1$
23. What is the degree of a cubic polynomial?
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$3$
24. What is the value of $\sqrt{225}$?
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$15$
25. Is $\sqrt{23}$ rational or irrational?
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Irrational.
26. What is the decimal expansion of $4\frac{1}{8}$?
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$4.125$ (terminating)
27. What is the value of $k$ if $(x-1)$ is a factor of $kx^2 - 3x + k$?
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$k = \frac{3}{2}$
28. What is the identity for $x^3 + y^3 + z^3 - 3xyz$?
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$\frac{1}{2}(x+y+z)[(x-y)^2 + (y-z)^2 + (z-x)^2]$
29. What is the value of $(9)^{\frac{3}{2}}$?
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$27$
30. What is the value of $(125)^{\frac{2}{3}}$?
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$25$
31. What is the value of $(16)^{\frac{3}{4}}$?
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$8$
32. What is the decimal form of $0.\overline{6}$ as a fraction?
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$\frac{2}{3}$
33. What is the value of $a + b + c$ if $5x + 2y = 2$ is written as $ax + by + c = 0$?
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$5$
34. What is the measure of $\angle BOC$ if $\angle AOC = (3x+10)^\circ$ and $\angle BOC = (4x-26)^\circ$ on a straight line?
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$86^\circ$
35. What is the value of $x$ if $\angle APQ = 50^\circ$ and $\angle PRD = 127^\circ$ with $AB \parallel CD$?
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$x = 50^\circ$ (alternate interior angle)
36. What is the value of $y$ if $\angle APQ = 50^\circ$ and $\angle PRD = 127^\circ$ with $AB \parallel CD$?
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$y = 77^\circ$
37. What is the value of $\angle QRS$ if $PQ \parallel ST$, $\angle PQR = 110^\circ$, and $\angle RST = 130^\circ$?
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$60^\circ$
38. What is the measure of $\angle XYQ$ if $\angle XYZ = 64^\circ$ and YQ bisects $\angle ZYP$?
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$122^\circ$
39. What is the reflex measure of $\angle QYP$ if $\angle XYZ = 64^\circ$ and YQ bisects $\angle ZYP$?
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$302^\circ$
40. What is the value of $x$ in $3x + 4y = 12$ when $x = 0$?
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$y = 3$
41. What is the quadrant of the point $(-4, -1)$?
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Quadrant III
42. What is the quadrant of the point $(2, -2)$?
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Quadrant IV
43. What is the location of the point $(-3, 0)$?
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On the $x$-axis
44. What is the location of the point $(0, 5)$?
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On the $y$-axis
45. What is the value of $P(0)$ for $P(x) = 5x - 4x^2 + 3$?
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$3$
46. Is $x = \frac{4}{5}$ a zero of $P(x) = 5x - \pi$?
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No, because $P(\frac{4}{5}) = 4 - \pi \ne 0$.
47. What is the value of $(3 + \sqrt{3})(2 + \sqrt{2})$?
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$6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$
48. What is the value of $2\sqrt{2} + 5\sqrt{3} + \sqrt{2} - \sqrt{3}$?
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$3\sqrt{2} + 4\sqrt{3}$
49. What is the decimal form of $\frac{1}{11}$?
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$0.\overline{09}$
50. What is the decimal form of $\frac{36}{100}$?
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$0.36$
51. What is the decimal form of $4\frac{1}{8}$?
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$4.125$
52. Classify $x^2 + x$ as linear, quadratic, or cubic.
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Quadratic
53. Classify $x - x^3$ as linear, quadratic, or cubic.
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Cubic
54. Classify $y^2 + y + 4$ as linear, quadratic, or cubic.
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Quadratic
55. Classify $1 + x$ as linear, quadratic, or cubic.
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Linear
56. Classify $3t$ as linear, quadratic, or cubic.
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Linear
57. Classify $r^2$ as linear, quadratic, or cubic.
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Quadratic
58. Classify $7x^3$ as linear, quadratic, or cubic.
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Cubic
59. Factorise $x^3 - 23x^2 + 142x - 120$.
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$(x-1)(x-10)(x-12)$
60. Verify $x^3 + y^3 = (x+y)(x^2 - xy + y^2)$.
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Expand RHS: $x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3 = x^3 + y^3$.
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