Arithmetic Sequences
The first 3 terms of a sequence are 4, 12 and 20. Write a recursive rule for the sequence.
Tn+1=Tn+8, T1=4
The first three terms of a sequence are 4, 20 and 100 respectively. Find the recursive rule for the sequence.
Tn+1=Tn x5, T1=4
Consider an arithmetic sequence with first term 16 and common difference 7. Find the sum of the first 10 terms of the sequence.
S10=475
Find the gradient of the line joining the points (1,5) and (-2,4)
m=1/3
Simplify (5x2y3)2
25x4y6
The third term and seventh term of an arithmetic sequence are 17 and 45 respectively. Find the recursive rule and the general rule for the sequence
Tn+1=Tn+7, T1=3
Tn=3+(n-1)7
The third and sixth terms of a geometric sequence are 18 and 486 respectively. Find the general rule for the sequence.
Tn=2x3n-1
The first term and common ratio of a sequence are 1 and 2.1 respectively. Find the sum of the first 10 terms of the sequence.
S10=1515.44 (2DP)
In triangle PQR, Q=48 degrees, R=68 degrees and r=18cm. Find the length of PR.
PR=14.43cm
Two fair, standard dice a rolled and the numbers are added. Determine the probability of obtaining a sum greater than six.
P(>6)=21/36
The first 3 terms of an arithmetic sequence are 143, 136 and 129 respectively. Find the number of terms that are greater than 0.
21 terms are greater than 0.
The first term and common ratio of a geometric sequence are 100 and 0.8 respectively. Find which term corresponds to 0.9223.
Term 22
The sum of the first n terms of an arithmetic sequence is given by Sn=3n2. Find the first term of the sequence and the common difference.
a=3 and d=6
Determine the coordinates of the first maximum and minimum values of y=-2sin(x+10). (degrees)
Minimum (80,-2)
Maximum (260,2)
A delegation of six students is to be selected from a group of 10 girls and 8 boys. Determine the probability that an even number of girls and boys are chosen.
0.3620 (4DP)
A special pool filter is installed to remove fine pollen particles from a pool situated in an area with a lot of trees. This filter removes 5,000 pollen particles from the water each day. If the pool has 162,000 pollen particles in the water, how many days will it take to completely filter the pool? (assuming no pollen is added).
34 days
The 3rd term and 5th term of a geometric sequence are -18 and -162 respectively. Find the 9th term after -13122.
-258280326
Farmers sometimes have land with soil that has a high salt content. To lower this salt content, and make the land usable for growing crops, trees are planted. To best fit the area with trees, the farmer has decided to plant them in rows with 5 trees in the first row, 8 in the second row, 11 in the third row and so on. How many trees will be planted if they plant 17 rows of trees?
493 trees
Given that f(x)=x-4, find the domain and range of g(x) given that g(x)=f(x2).
x is an element of all real numbers
y is greater than or equal to -4.
A mole of helium gas weighs approximately 4 grams and has approximately 6x1023 helium atoms. WITHOUT USING A CALCULATOR find, in scientific notation and correct to 3 significant figures, the weight of one helium atom.
6.67x10-24
Bruce invests $30,000 into a bank account that pays 3.5% simple interest per year. The interest is paid at the end of each year and is not added to the principal. Let B(n) be the account balance at the end of n years.
Find the minimum number of years for the account balance to exceed $45,000.
16 years
Peter hopes to save enough money to buy himself a new computer. In his plan, which covers a period of a fortnight, he saves 10c on the first day, 20c on the second day, 40c on the third day etc. On which day would he save $3.20?
Day 6
A toad hopes 200m along an outback highway on the first night. The distance hopped each night is 1% less than the distance hopped the previous night. Will the toad be able to reach a roadhouse 25km away from where it started hopping? Show working and justify your answer
No, 0.99n=-0.25 has no real solutions. i.e. a positive number to a power can not equal a negative number. This means that the sum of the toads distances does not exceed 25,000m before his distance per night reaches 0m.
Complete the square for 2x2+8x-9. Hence find the exact solutions of the quadratic equation.
x=-2+sqrt(17/2)
x=-2-sqrt(17/2)
Simplify ((2+x)3-(2+x)2)/(2+x)3
(1+x)/(2+x)