Daily Practice · Higher Plus
April 1963 5-a-day
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The batch download puts all 5 tiers' April 1963 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1963In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 2nd April 1963The probability of winning a game is 4/5. A player expects 72 wins. How many games did they play?
- 3rd April 1963On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th April 1963Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 5th April 1963Solve 4x^2 - x - 3 = 0.
- 6th April 1963y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 7th April 1963In a vector proof you find that vector PQ = 3a - 4b and vector RS = 6a - 8b. What does this show about PQ and RS?
- 8th April 1963A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 9th April 1963A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 10th April 1963A rectangle is 23 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th April 1963f(x) = 6x - 7. Work out the inverse function f^-1(x).
- 12th April 1963y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 81.
- 13th April 1963A cuboid measures 10 cm by 4 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th April 1963A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th April 1963On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th April 1963Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 17th April 1963Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 18th April 1963A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 19th April 1963A cuboid measures 13 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th April 1963A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st April 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 22nd April 1963A block has mass 800 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd April 1963Use the iteration x(n+1) = cube root of (11x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.
- 24th April 1963y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 25th April 1963The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 26th April 1963A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 27th April 1963On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th April 1963x = 51 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th April 1963Work out the nth term of the quadratic sequence 7, 19, 37, 61, ...
- 30th April 1963y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.