Daily Practice · Higher Plus
April 1968 5-a-day
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The batch download puts all 5 tiers' April 1968 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1968A block has mass 460 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd April 1968Make x the subject of 8x + 7 = y(x + 7).
- 3rd April 1968y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 4th April 1968In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th April 1968The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 6th April 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 7th April 1968x = 108 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th April 1968Write 6/(x - 2) + 7/(x + 4) as a single fraction.
- 9th April 1968y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 36.
- 10th April 1968In a vector proof you find that vector PQ = 2a + 3b and vector RS = 10a + 15b. What does this show about PQ and RS?
- 11th April 1968A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 12th April 1968On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th April 1968A car covers 120 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th April 1968Solve 2x^2 - 5x + 3 = 0.
- 15th April 1968A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 16th April 1968A cuboid measures 13 cm by 6 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th April 1968A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th April 1968A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 19th April 1968Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 20th April 1968f(x) = 4x + 1. Work out the inverse function f^-1(x).
- 21st April 1968y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 22nd April 1968A cuboid measures 10 cm by 8 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd April 1968A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th April 1968On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th April 1968Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 26th April 1968Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 27th April 1968y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 28th April 1968The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 29th April 1968A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 30th April 1968A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?