Daily Practice · Higher Plus
August 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1994A block has mass 530 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd August 1994Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 3rd August 1994y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 4th August 1994A cuboid measures 6 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th August 1994A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th August 1994On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th August 1994x = 47 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th August 1994Work out the nth term of the quadratic sequence 4, 11, 24, 43, ...
- 9th August 1994y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 10th August 1994The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 11th August 1994A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 12th August 1994A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 13th August 1994A car covers 410 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.
- 14th August 1994The point (1, -5) lies on y = f(x). Write down its image on y = f(x + 6).
- 15th August 1994y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 49.
- 16th August 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.
- 17th August 1994The probability of winning a game is 3/4. A player expects 72 wins. How many games did they play?
- 18th August 1994On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th August 1994Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 20th August 1994Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 21st August 1994A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd August 1994In a vector proof you find that vector PQ = 5a - 4b and vector RS = 10a - 8b. What does this show about PQ and RS?
- 23rd August 1994A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 24th August 1994A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 25th August 1994Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 26th August 1994f(x) = 2x - 8 and g(x) = 6x + 4. Work out fg(2).
- 27th August 1994y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 28th August 1994A cuboid measures 9 cm by 3 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th August 1994A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th August 1994On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st August 1994A rectangle is 27 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.