Daily Practice · Higher Plus
August 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1996A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 2nd August 1996Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 3rd August 1996Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 4th August 1996y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 4.
- 5th August 1996In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 6th August 1996The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 7th August 1996On 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?
- 8th August 1996Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 9th August 1996f(x) = 2x + 8 and g(x) = 2x - 7. Work out fg(4).
- 10th August 1996A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 11th August 1996In a vector proof you find that vector PQ = 4a - 6b and vector RS = 8a - 12b. What does this show about PQ and RS?
- 12th August 1996A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 13th August 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 14th August 1996A rectangle is 22 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th August 1996The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 16th August 1996y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 17th August 1996A cuboid measures 5 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th August 1996A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th August 1996On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th August 1996Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 21st August 1996A quadratic sequence starts 4, 7, 14, 25. Work out the second difference, and the coefficient of n^2.
- 22nd August 1996y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 23rd August 1996A cuboid measures 8 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th August 1996A bag holds 5 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th August 1996A 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?
- 26th August 1996A block has mass 430 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th August 1996Solve x^2 + 4x - 5 > 0.
- 28th August 1996y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 49.
- 29th August 1996The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 30th August 1996A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 31st August 1996On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?