Daily Practice · Higher Plus
April 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1993 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1993On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd April 1993Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 3rd April 1993f(x) = 2x + 4 and g(x) = 2x - 6. Work out fg(1).
- 4th April 1993A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 5th April 1993A cuboid measures 4 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th April 1993A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th April 1993A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 8th April 1993Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 9th April 1993The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 10th April 1993y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 11th April 1993A cuboid measures 12 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th April 1993A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th April 1993On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th April 1993A rectangle is 17 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th April 1993A quadratic sequence starts 15, 28, 47, 72. Work out the second difference, and the coefficient of n^2.
- 16th April 1993y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 17th April 1993The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 18th April 1993A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 19th April 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 20th April 1993Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 21st April 1993Solve x^2 + 7x + 12 < 0.
- 22nd April 1993y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 25.
- 23rd April 1993In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 24th April 1993The probability of winning a game is 1/2. A player expects 8 wins. How many games did they play?
- 25th April 1993On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th April 1993A block has mass 370 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.
- 27th April 1993Write x^2 - 6x + 2 in the form (x + a)^2 + b.
- 28th April 1993A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 29th April 1993In a vector proof you find that vector PQ = 6a + 3b and vector RS = 18a + 9b. What does this show about PQ and RS?
- 30th April 1993A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.