Daily Practice · Higher Plus
August 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2006A cuboid measures 13 cm by 14 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd August 2006A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd August 2006On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th August 2006Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 5th August 2006Use the iteration x(n+1) = cube root of (9x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.
- 6th August 2006A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 7th August 2006The 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.
- 8th August 2006A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 9th August 2006A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 10th August 2006Simplify sqrt(12) + sqrt(12), giving your answer in the form a sqrt(b).
- 11th August 2006Work out the nth term of the quadratic sequence -5, -3, 1, 7, ...
- 12th August 2006y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 13th August 2006In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 14th August 2006The probability of winning a game is 1/4. A player expects 2 wins. How many games did they play?
- 15th August 2006On 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?
- 16th August 2006A rectangle is 25 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th August 2006The point (-4, -2) lies on y = f(x). Write down its image on y = f(x - 1).
- 18th August 2006y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 19th August 2006In a vector proof you find that vector PQ = 3a + 5b and vector RS = 15a + 25b. What does this show about PQ and RS?
- 20th August 2006A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 21st August 2006A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 22nd August 2006Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 23rd August 2006Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 24th August 2006y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 49.
- 25th August 2006A cuboid measures 10 cm by 6 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th August 2006A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th August 2006On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th August 2006A block has mass 840 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th August 2006f(x) = 6x - 1 and g(x) = 4x + 1. Work out fg(0).
- 30th August 2006A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 31st August 2006A cuboid measures 4 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.