Daily Practice · Higher Plus
April 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1978 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1978A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd April 1978A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 3rd April 1978A block has mass 430 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th April 1978Work out the coordinates of the turning point of y = x^2 + 2x + 8.
- 5th April 1978y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 4.
- 6th April 1978The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 7th April 1978A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 8th April 1978On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th April 1978x = 130 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th April 1978Simplify (x^2 + 14x + 48)/(x + 6).
- 11th April 1978A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 12th April 1978In 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.
- 13th April 1978The probability of winning a game is 4/5. A player expects 16 wins. How many games did they play?
- 14th April 1978A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 15th April 1978A car covers 630 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th April 1978In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 17th April 1978y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 18th April 1978In a vector proof you find that vector PQ = a - 4b and vector RS = 5a - 20b. What does this show about PQ and RS?
- 19th April 1978A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 20th April 1978On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st April 1978Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 22nd April 1978Make x the subject of 7x + 6 = y(x + 6).
- 23rd April 1978y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 24th April 1978A cuboid measures 3 cm by 6 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th April 1978A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th April 1978A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 27th April 1978Simplify sqrt(50) + sqrt(2), giving your answer in the form a sqrt(b).
- 28th April 1978Write 4/(x - 5) + 4/(x + 2) as a single fraction.
- 29th April 1978y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 16.
- 30th April 1978A cuboid measures 12 cm by 9 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.