Daily Practice · Higher Plus
May 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1994A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd May 1994On 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?
- 3rd May 1994Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 4th May 1994The point (0, -1) lies on y = f(x). Write down its image on y = f(x + 5).
- 5th May 1994y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 6th May 1994A cuboid measures 5 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th May 1994A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th May 1994A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 9th May 1994A block has mass 290 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.
- 10th May 1994Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 11th May 1994y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 64.
- 12th May 1994The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 13th May 1994A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 14th May 1994On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th May 1994x = 47 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th May 1994f(x) = 3x + 1 and g(x) = 4x + 1. Work out fg(4).
- 17th May 1994A train slows steadily from 38 m/s to rest in 8 seconds. Work out its deceleration.
- 18th May 1994In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 19th May 1994The probability of winning a game is 1/4. A player expects 4 wins. How many games did they play?
- 20th May 1994A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 21st May 1994A car covers 800 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.
- 22nd May 1994The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 23rd May 1994y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 24th May 1994In a vector proof you find that vector PQ = 6a - 3b and vector RS = 12a - 6b. What does this show about PQ and RS?
- 25th May 1994A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 26th May 1994On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th May 1994Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 28th May 1994A quadratic sequence starts 5, 16, 37, 68. Work out the second difference, and the coefficient of n^2.
- 29th May 1994y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 30th May 1994A cuboid measures 13 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st May 1994A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?