Daily Practice · Higher Plus
July 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1994On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd July 1994A car covers 610 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd July 1994Make x the subject of 4x + 7 = y(x + 7).
- 4th July 1994A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 5th July 1994A cuboid measures 13 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th July 1994A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th July 1994A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 8th July 1994Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 9th July 1994Write 6/(x - 6) + 7/(x + 5) as a single fraction.
- 10th July 1994y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 11th July 1994The 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.
- 12th July 1994A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 13th July 1994On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th July 1994Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 15th July 1994Solve 2x^2 + 5x - 12 = 0.
- 16th July 1994y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 17th July 1994In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 18th July 1994The probability of winning a game is 3/10. A player expects 27 wins. How many games did they play?
- 19th July 1994A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 20th July 1994A rectangle is 26 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st July 1994f(x) = 6x - 8. Work out the inverse function f^-1(x).
- 22nd July 1994y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 64.
- 23rd July 1994In a vector proof you find that vector PQ = 4a - 2b and vector RS = 12a - 6b. What does this show about PQ and RS?
- 24th July 1994A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 25th July 1994On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th July 1994Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 27th July 1994Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 28th July 1994A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.
- 29th July 1994A cuboid measures 3 cm by 14 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th July 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?
- 31st July 1994A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?