Daily Practice · Higher Plus
April 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1994 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1994A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd April 1994A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 3rd April 1994x = 78 and y = 39, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th April 1994Solve 4x^2 - 13x + 10 = 0.
- 5th April 1994y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 6th April 1994A cuboid measures 11 cm by 14 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th April 1994A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th April 1994On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th April 1994A car covers 130 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th April 1994f(x) = 6x + 3. Work out the inverse function f^-1(x).
- 11th April 1994y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 12th April 1994The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 13th April 1994A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 14th April 1994A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 15th April 1994Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 16th April 1994Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 17th April 1994y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 25.
- 18th April 1994In 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.
- 19th April 1994The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 20th April 1994On 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?
- 21st April 1994Simplify sqrt(75) + sqrt(48), giving your answer in the form a sqrt(b).
- 22nd April 1994Use the iteration x(n+1) = cube root of (5x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 23rd April 1994A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 24th April 1994In a vector proof you find that vector PQ = a + 4b and vector RS = 5a + 20b. What does this show about PQ and RS?
- 25th April 1994A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 26th April 1994A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 27th April 1994A rectangle is 4 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th April 1994Work out the nth term of the quadratic sequence 14, 24, 38, 56, ...
- 29th April 1994y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 30th April 1994A cuboid measures 14 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.